The 34-year-old Northern Ireland captain looks set to return to Ibrox, having left to sign for Saints during the summer of 2012.

Davis has found his first-team chances limited this season, and Hasenhuttl revealed the club would look to support the midfielder in his desire to move back to Scotland.

"The fact is he has a half-a-year contract here until the summer, so what we want to give him is a chance to make the next step. If there is a possibility, then we will help him to do so," Hasenhuttl said at a press conference.

"He has done a lot for this club, and there we find a good solution where we have a win-win situation for both sides."

Asked if the deal was close to completion in the next few days, the Saints boss added: "It can be. I am looking forward and if it is, then we will tell you."

Should the deal progress as planned, Davis is expected to join up with Steven Gerrard's squad at a warm-weather training camp in Tenerife before the domestic Scottish programme resumes later in January.

Southampton battled to a goalless draw at Chelsea on Wednesday night, but found themselves dropping into the bottom three following Burnley's win at Huddersfield.

Hasenhuttl revealed he expected to trim his squad during the January window, as well as targeting potential reinforcements to fit in with his "philosophy".

Italian forward Manolo Gabbiadini is another player linked with a move away.

Hasenhuttl said: "The fact is our squad at the moment is too big and we have to sell players and he (Gabbiadini) is one other clubs are interested in, so it can be in the next few weeks or days, it can happen he would be transferred.

"We see there are a few problems we have in our squad, for my kind of football, for my philosophy in a few positions, I need more speed, more running quality, therefore we will need also new players.

"What we do now is first look to (make) the big squad a little bit smaller and then we will have a look if we find someone who helps us to move our deficits away."

Hasenhuttl added: "We are open-minded and our eyes are open, so we know in the winter period it is not so easy to find transfers that really help you.

"If we do something it must also be for the future, although we need it now, it only makes sense if it helps us for a longer period.

"It should be a player who is not too old, but fits perfectly in our philosophy and then it can be possible that we do something, yes"

Southampton will be in FA Cup action on Saturday when they travel to Sky Bet Championship promotion-hopefuls Derby.

Defender Maya Yoshida will be away with Japan for the Asia Cup, but full-back Matt Targett should be in contention after being rested because of a thigh problem.